The study will be performed as a randomized 12 weeks controlled, cross-over trial, which will address the effects on T2D of an isoenergetic low carbohydrate diet (carbohydrate 30 E%, protein 30 E%, fat 40 E%) compared to an isoenergetic control diet (carbohydrate 50 E%, protein 17 E%, fat 33 E%) currently recommended to individuals with T2D. The study is extended with 24 weeks on an isoenergetic low carbohydrate diet to examine the prolonged effect of the experimental diet on T2D and its pathophysiology. To test the hypothesis that the isoenergetic control diet is detrimental to glucose metabolism after only a short transition to this diet, the participants are reinforced to eat that diet during 6 weeks after the 24 weeks on low carbohydrate/high protein diet.